Question

A sum of money is borrowed and paid back in two annual instalments of Rs. $882$ each allowing $5\%$ compound interest. The sum borrowed was ________.

• A. Rs. $1620$
• B. Rs. $1640$
• C. Rs. $1680$
• D. Rs. $1700$

Answer 1

The correct option is B Rs. $1640$

Given:

Money is paid in two annual installments of Rs $882$.

$\therefore$ Total Amount paid $=2\times 882=1764$

Now,

Let the sum be $x$

Interest of first Year $=\frac{x\times 5\times 1}{100}$

$=0.05x$

Standing Amount After first year$=x+0.05x=1.05x$

After paying $Rs882$ (first Installment) Standing Principal for second year$=(1.05x-882)$

Now,

Interest of Second Year $=\frac{(1.05x-882)\times 5\times 1)}{100}$

Standing Amount at the end of second year $(1.05x-882)+\frac{(1.05x-882)\times 5\times 1}{100}=882$

$⟹(1.05x-882)\times 100+(1.05x-882)\times 5=882\times 100$

$⟹105\times \left(1.05x\right)-105\times 882=882\times 100$

$⟹105\times \left(1.05x\right)=882\times 205$

$⟹x=\frac{882\times 205}{105\times 1.05}$

$⟹x=1640$